Quantum fluctuations in a scale-free network-connected Ising system

Rafael Alves Dumer, Maurício Godoy

Hangmo Yi

We study the effect of quantum fluctuations on the critical behavior of the Ising ferromagnetic phase transitions that do not belong to the mean-field universality class. A model system is considered, in which Ising spins are placed on the nodes of a scale-free network. Our Monte Carlo analysis shows that the critical exponents differ from those of mean-field phase transitions when degree exponent gamma is in the range 3<gamma<5 . This confirms earlier analytic calculations based on ansatzes and approximation methods. As we apply quantum fluctuations by means of a magnetic field perpendicular to the Ising spin direction, the transition temperature T(c) decreases with increasing magnetic field strength. We find, however, that the quantum fluctuations do not alter the critical exponents and the universality class remains unchanged.

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

Takuma Tanaka, Hirokazu Fujisaka, Masayoshi Inoue

Free-energy fluctuations in a one-dimensional dilute Ising system in the low dilution case are studied from the fluctuation-spectrum standpoint by discussing how the position-to-position fluctuation of free energy arises as magnetic bonds are gradually replaced by non-magnetic ones. The fluctuation-strength monotonically increases as the ratio of dilution is increased. This is found to be described as the scaling laws of relevant functions characteristic of the fluctuation-spectrum analysis.

Jamir Marino, Alessandro Silva